Problem: Rewrite as a simplified fraction. ${1.20\overline{7} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1207.7777...\\ 100x &= 120.7777...\end{align*}}$ Subtracting the two equations, we have: ${900x = 1087}$ ${x = \dfrac{1087}{900}} \text{or} {1 \dfrac{187}{900}}$